arXiv subjects

Irène Casseli

Publications and source records attributed to Irène Casseli.

2 recordsLinked to original sources

arXiv2019

Fixed points of the Berezin transform of polyanlytic Fock spaces

We study the fixed points of the Berezin transform in polyanalytic Fock spaces of $\mathbb{C}$. We show that an $L^p$ function, $p\in[1,+\infty]$, with respect to the Lebesgue measure is invariant under this transformation if and only if it is harmonic. From this we deduce that the only bounded fixed points of the Berezin transform of polyanalytic Fock spaces are constant functions.

math.FA↗

arXiv2018

On products of some Toeplitz operators on polyanalytic Fock spaces

The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $ T_{f}T_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.

math.CV↗